Pipes A and B can fill a tank in 15 hours and 12 hours, respectively. Pipe C alone can empty the full tank in 10 hours. If all the three pipes are opened together for 2 hours 40 minutes, then what part of the tank will remain unfilled?

A

$$\frac{3}{20}$$

B

$$\frac{13}{15}$$

C

$$\frac{2}{15}$$

D

$$\frac{17}{20}$$